by Zhang, Shouchuan; Zhang, Yao-Zhong

It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {e

_ii
}
_I
with each ē

_ii
in the center of $\bar \Lambda = \Lambda/r$ if Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given. As a corollary, Λ is a finite algebra with non-zero unity element over a perfect field k (e.g., a field with characteristic zero or a finite field) if Λ is isomorphic to a generalized path algebra k (D, Ω, ρ) of finite directed graph with weak relations and dim < ∞; Λ is a generalized elementary algebra which can be lifted with nilpotent Jacobson radical and has a complete set of pairwise orthogonal idempotents if Λ is isomorphic to a path algebra with relations.

DOI: 10.1007/s10468-006-9036-z
Online Date: 12/19/2006
Print publication date: 4/1/2007
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